Re: College Algebra - Volunteers Wanted

Is that the newest Pythagoras story. I have read at least 6 or 7 different renditions of that. I think this one is pretty good. Hippasus got what he deserved. If only they hadn't discovered those darn irrational numbers. Why couldn't they have just defined that hypotenuse as almost 3 / 2 units? Probably wouldn't have needed square roots and all that i jazz either.

In mathematics, you don't understand things. You just get used to them.

Re: College Algebra - Volunteers Wanted

You can sometimes work out the degree of an expression by dividing ...

I like the idea of numerical experimentation as a means of getting an answer that can later be proved rigorously.

I noticed that you use 2,4,10,100,1000... to try to determine the limit of ln (3 + √ x) / ln(x). I got embarrassed once when I did the same procedure to guess at a limit. Because I used all even numbers my limit appeared to converge on 1 / 2. What I didn't see was that for odd values it converged to - 1 / 2. Using all even numbers for x ( doesn't matter in your example ) can cause sign errors. So putting some odd numbers in there eliminates that possibility.

Really nice animations!

In mathematics, you don't understand things. You just get used to them.

Re: College Algebra - Volunteers Wanted

Re frac(x) where x = -3.65:

I tested this on my two scientific calculators that have the frac function...an HP 48SX and a Canon F-802P.

Both say this:frac(x) = -.65int(x) = -3 int(x) + frac(x) = -3.65

My first inclination, which no doubt stems from my use of these calculators, is that both the frac and int functions should simply select their particular side of the decimal point and maintain the sign. I don't know what is generally thought or taught, but to me it seems the intuitive approach.

Re: College Algebra - Volunteers Wanted

Hi all;

There isn't any general agreement on how to handle frac(-3.65). Most calculators and CAS are in favor of -.65 while most books and sites are favoring .35. A small note to warn the reader about the ambiguity would be a good idea.

In mathematics, you don't understand things. You just get used to them.

Re: College Algebra - Volunteers Wanted

Thanks phrontister,

I went for most of your suggestions, but instead of "(the same as the Ceiling function)" I went with "(the rule is: neighbouring integer closest to zero, or "just throw away the .65")", as that is the rule they follow for positive and negative.

We have kept it short, sweet and hopefully accurate

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Re: College Algebra - Volunteers Wanted

I was just mentioning it so that you would know, if you think you should change it then:

The relationship looks like this:

So when [H+] is 10^(-7) then - log (10^-7) = 7 a neutral ph. As [H+] goes up [OH-] goes down.

You can use either of these for accuracy.

Use either of those just as long as in your opinion it does not confuse the reader.Just phrase it as - log of the molar concentration of the hydronium ion or the hydrogen ion for H30+ or H+ respectively. You see in math [ ] is for grouping but in chemistry [ ] this means molar concentration( moles per liter ).

In mathematics, you don't understand things. You just get used to them.